Problem: In $1950$, the per capita gross domestic product (GDP) of Australia was approximately $\$1800$. Each year afterwards, the per capita GDP increased by approximately $6.7\%$. Write a function that gives the approximate per capita GDP $G(t)$ of Australia $t$ years after $1950$. Do not enter commas in your answer. $G(t)=$
Answer: Increasing at a rate of $6.7\%$ means the per capita GDP keeps its $100\%$ and adds $6.7\%$ more, for a total of $106.7\%$. So each year, the per capita GDP is multiplied by $106.7\%$, which is the same as a factor of $1.067$. If we start with the initial per capita GDP, $\$1800$, and keep multiplying by $1.067$, this function gives us the approximate per capita GDP $G(t)$ of Australia $t$ years after $1950$ : $G(t)=1800\cdot1.067^t$